SACRAMENTO -- One Republican candidate for governor is a former U.S. treasury official, a moderate who promises to create jobs and fix California's public school system. Another is a firebrand -- a conservative California assemblyman and former anti-immigrant "Minuteman" who was convicted of a misdemeanor in 2012 for having a loaded gun in his carry-on luggage at Ontario airport.

Although some California Republican leaders had seen the moderate, Neel Kashkari, as the GOP's candidate of the future in a deep blue state, tea party favorite Tim Donnelly is pummeling him, according to a surprising new Field Poll.

Thirty-four percent of likely Republican voters would pick Donnelly, R-Hesperia, while only 3 percent would vote for Kashkari.

Not surprising is that the poll finds Democratic Gov. Jerry Brown will win the June 3 open primary in a landslide, with his approval rating soaring to an all-time high of 59 percent of California voters.

Even though no Republican is likely to give Brown a true challenge in a one-on-one battle in November, the new poll suggests the California GOP continues to drift farther from the mainstream and is increasingly losing relevance as the state grows more diverse and more Democratic.

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"This is a battle for the soul of the Republican Party," said Larry Gerston, a political-science professor at San Jose State. "If Donnelly prevails, it indicates that the fiscal conservatives, the evangelical conservatives and the tea party conservatives control the party and leave Republicans with little opportunity to succeed in the long run. If Kashkari can break through, it would be a sea change, and for the first time in 30 years, the party would show that it has some control of the middle."

Jim Brulte, the GOP's state party chairman who is trying to push Republicans toward the center, declined comment on Tuesday.

Brown was the choice of 57 percent of likely voters surveyed. Donnelly came in second with 17 percent, followed by Laguna Beach Mayor Andrew Blount (who has barely campaigned) at 3 percent and Kashkari at 2 percent. Twenty percent were still undecided.

With eight weeks to go until the primary election, Kashkari's campaign still needs several million dollars to launch any kind of effective statewide advertising campaign.

So far, he has raised considerably more money than other Republican candidates, and he has been actively campaigning up and down the state. He has about $903,000 in the bank, while Blount and Donnelly have about $8,000 and $10,000, respectively.

Brown, meanwhile, has amassed a war chest of close to $20 million.

Donnelly has been running a low-budget campaign since he announced his candidacy two years ago. And he's been "a genius" at reaching voters through social media and on websites like YouTube, where he has posted quirky campaign videos that have gone viral, said Allan Hoffenblum, publisher of the California Target Book, which handicaps legislative and congressional races.

Having a double-digit lead on his closest Republican challenger is "pretty encouraging," said Donnelly, who takes pride in the fact that his campaign "hasn't spent a cent on persuasion."

"There's a movement in California to unite under the banner of liberty, freedom, civil rights and privacy, and I'm leading it," Donnelly said. "I'm the underdog, but I like to call myself the underdog frontrunner."

But Hoffenblum said the poll might have an unintended, adverse effect on Donnelly's campaign because there is fear among establishment Republicans about how Donnelly's success will reflect on the chances of other GOP candidates in November.

"Donnelly has strong views on guns and immigration," Hoffenblum said. "If he's at the top of the ticket, it could do tremendous harm for people" like Rep. Jeff Denham, R-Modesto, who is locked in a tight race for re-election in his Central Valley swing district.

The Field Poll surveyed 1,000 registered voters between March 18 and April 5, including 504 voters considered likely to vote in June's primary -- in which the two top candidates, regardless of party, will advance to November. The survey has a margin of error of plus or minus 3.2 percentage points among registered voters and plus or minus 4.5 percentage points among likely voters.

Some political analysts said it's obviously an uphill fight for Kashkari, but he should not be counted out.

"Most voters don't know anything about Neel Kashkari other than that he has a strange-sounding name," Hoffenblum said. "This poll shows that Kashkari hasn't made any impact yet, but he also hasn't really tried or spent any money."

Maybe one encouraging sign for Kashkari is that most Californians don't seem to know much at this point about any of the GOP candidates for governor.

Half of likely voters surveyed have no opinion of Donnelly, 64 percent have no opinion of Kashkari and 71 percent have no opinion of Blount. Conversely, only 4 percent of voters have no opinion of Brown.

"We're confident we'll have the resources to communicate Neel's message of jobs and education to voters and ultimately earn their support," said Jessica Hsiang Ng, a spokeswoman for Kashkari's campaign.

But $903,000 isn't enough money to purchase the TV commercials he would need to boost his name recognition among likely voters, said Bill Whalen, a Hoover Institution fellow and a former aide to Republican Gov. Pete Wilson.

"If Kashkari wants to be successful, he'll have to find very creative ways to get out the vote on his behalf. He'll have to use social media and other tools that don't cost a lot of money," Whalen said. "Donnelly isn't uncatchable at 15 points ahead. Stranger things have happened."